IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i5p801-d358330.html
   My bibliography  Save this article

Global Stability Analysis of Fractional-Order Quaternion-Valued Bidirectional Associative Memory Neural Networks

Author

Listed:
  • Usa Humphries

    (Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru 10140, Thailand)

  • Grienggrai Rajchakit

    (Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 50290, Thailand)

  • Pramet Kaewmesri

    (Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru 10140, Thailand)

  • Pharunyou Chanthorn

    (Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Ramalingam Sriraman

    (Department of Science and Humanities, Vel Tech High Tech Dr. Rangarajan Dr. Sakunthala Engineering College, Avadi, Tamil Nadu 600 062, India)

  • Rajendran Samidurai

    (Department of Mathematics, Thiruvalluvar University, Vellore, Tamil Nadu 632115, India)

  • Chee Peng Lim

    (Institute for Intelligent Systems Research and Innovation, Deakin University, Waurn Ponds, VIC 3216, Australia)

Abstract

We study the global asymptotic stability problem with respect to the fractional-order quaternion-valued bidirectional associative memory neural network (FQVBAMNN) models in this paper. Whether the real and imaginary parts of quaternion-valued activation functions are expressed implicitly or explicitly, they are considered to meet the global Lipschitz condition in the quaternion field. New sufficient conditions are derived by applying the principle of homeomorphism, Lyapunov fractional-order method and linear matrix inequality (LMI) approach for the two cases of activation functions. The results confirm the existence, uniqueness and global asymptotic stability of the system’s equilibrium point. Finally, two numerical examples with their simulation results are provided to show the effectiveness of the obtained results.

Suggested Citation

  • Usa Humphries & Grienggrai Rajchakit & Pramet Kaewmesri & Pharunyou Chanthorn & Ramalingam Sriraman & Rajendran Samidurai & Chee Peng Lim, 2020. "Global Stability Analysis of Fractional-Order Quaternion-Valued Bidirectional Associative Memory Neural Networks," Mathematics, MDPI, vol. 8(5), pages 1-27, May.
  • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:801-:d:358330
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/5/801/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/8/5/801/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Nallappan Gunasekaran & Guisheng Zhai, 2020. "Sampled-data state-estimation of delayed complex-valued neural networks," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(2), pages 303-312, January.
    2. Tu, Zhengwen & Yang, Xinsong & Wang, Liangwei & Ding, Nan, 2019. "Stability and stabilization of quaternion-valued neural networks with uncertain time-delayed impulses: Direct quaternion method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    3. Cao, Yang & Samidurai, R. & Sriraman, R., 2019. "Robust passivity analysis for uncertain neural networks with leakage delay and additive time-varying delays by using general activation function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 57-77.
    4. Goh, S.L. & Chen, M. & Popović, D.H. & Aihara, K. & Obradovic, D. & Mandic, D.P., 2006. "Complex-valued forecasting of wind profile," Renewable Energy, Elsevier, vol. 31(11), pages 1733-1750.
    5. Tu, Zhengwen & Zhao, Yongxiang & Ding, Nan & Feng, Yuming & Zhang, Wei, 2019. "Stability analysis of quaternion-valued neural networks with both discrete and distributed delays," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 342-353.
    6. Samidurai, R. & Sriraman, R., 2019. "Robust dissipativity analysis for uncertain neural networks with additive time-varying delays and general activation functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 201-216.
    7. Pratap, A. & Raja, R. & Cao, J. & Rihan, Fathalla A. & Seadawy, Aly R., 2020. "Quasi-pinning synchronization and stabilization of fractional order BAM neural networks with delays and discontinuous neuron activations," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    8. Park, Ju H., 2008. "On global stability criterion of neural networks with continuously distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 444-449.
    9. Qi, Xingnan & Bao, Haibo & Cao, Jinde, 2019. "Exponential input-to-state stability of quaternion-valued neural networks with time delay," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 382-393.
    10. Yongkun Li & Xiaofang Meng & Yuan Ye, 2018. "Almost Periodic Synchronization for Quaternion-Valued Neural Networks with Time-Varying Delays," Complexity, Hindawi, vol. 2018, pages 1-13, April.
    11. R. Sriraman & R. Samidurai, 2019. "Global asymptotic stability analysis for neutral-type complex-valued neural networks with random time-varying delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 50(9), pages 1742-1756, July.
    12. Wang, Tianyu & Zhu, Quanxin, 2019. "Stability analysis of stochastic BAM neural networks with reaction–diffusion, multi-proportional and distributed delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C).
    13. Grienggrai Rajchakit & Pharunyou Chanthorn & Pramet Kaewmesri & Ramalingam Sriraman & Chee Peng Lim, 2020. "Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks," Mathematics, MDPI, vol. 8(3), pages 1-29, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rajchakit, G. & Sriraman, R. & Lim, C.P. & Unyong, B., 2022. "Existence, uniqueness and global stability of Clifford-valued neutral-type neural networks with time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 508-527.
    2. Zhang, Zhengqiu & Yang, Zhen, 2023. "Asymptotic stability for quaternion-valued fuzzy BAM neural networks via integral inequality approach," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    3. Wang, Chen & Zhang, Hai & Ye, Renyu & Zhang, Weiwei & Zhang, Hongmei, 2023. "Finite time passivity analysis for Caputo fractional BAM reaction–diffusion delayed neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 424-443.
    4. Chen, Dazhao & Zhang, Zhengqiu, 2022. "Finite-time synchronization for delayed BAM neural networks by the approach of the same structural functions," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    5. Gan, Binbin & Chen, Hao & Xu, Biao & Kang, Wei, 2023. "A norm stability condition of neutral-type Cohen-Grossberg neural networks with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Usa Humphries & Grienggrai Rajchakit & Pramet Kaewmesri & Pharunyou Chanthorn & Ramalingam Sriraman & Rajendran Samidurai & Chee Peng Lim, 2020. "Stochastic Memristive Quaternion-Valued Neural Networks with Time Delays: An Analysis on Mean Square Exponential Input-to-State Stability," Mathematics, MDPI, vol. 8(5), pages 1-26, May.
    2. Grienggrai Rajchakit & Pharunyou Chanthorn & Pramet Kaewmesri & Ramalingam Sriraman & Chee Peng Lim, 2020. "Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks," Mathematics, MDPI, vol. 8(3), pages 1-29, March.
    3. Rajchakit, G. & Sriraman, R. & Lim, C.P. & Unyong, B., 2022. "Existence, uniqueness and global stability of Clifford-valued neutral-type neural networks with time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 508-527.
    4. Cao, Yang & Sriraman, R. & Shyamsundarraj, N. & Samidurai, R., 2020. "Robust stability of uncertain stochastic complex-valued neural networks with additive time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 207-220.
    5. Pharunyou Chanthorn & Grienggrai Rajchakit & Jenjira Thipcha & Chanikan Emharuethai & Ramalingam Sriraman & Chee Peng Lim & Raja Ramachandran, 2020. "Robust Stability of Complex-Valued Stochastic Neural Networks with Time-Varying Delays and Parameter Uncertainties," Mathematics, MDPI, vol. 8(5), pages 1-19, May.
    6. Li, Liangchen & Xu, Rui & Lin, Jiazhe, 2020. "Lagrange stability for uncertain memristive neural networks with Lévy noise and leakage delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    7. Zhang, Zhengqiu & Yang, Zhen, 2023. "Asymptotic stability for quaternion-valued fuzzy BAM neural networks via integral inequality approach," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    8. Pan, Jie & Pan, Zhaoya, 2021. "Novel robust stability criteria for uncertain parameter quaternionic neural networks with mixed delays: Whole quaternionic method," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    9. Harshavarthini, S. & Sakthivel, R. & Ma, Yong-Ki & Muslim, M., 2020. "Finite-time resilient fault-tolerant investment policy scheme for chaotic nonlinear finance system," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    10. Tu, Zhengwen & Yang, Xinsong & Wang, Liangwei & Ding, Nan, 2019. "Stability and stabilization of quaternion-valued neural networks with uncertain time-delayed impulses: Direct quaternion method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    11. Shu, Jinlong & Wu, Baowei & Xiong, Lianglin & Wu, Tao & Zhang, Haiyang, 2021. "Stochastic stabilization of Markov jump quaternion-valued neural network using sampled-data control," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    12. Iswarya, M. & Raja, R. & Cao, J. & Niezabitowski, M. & Alzabut, J. & Maharajan, C., 2022. "New results on exponential input-to-state stability analysis of memristor based complex-valued inertial neural networks with proportional and distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 440-461.
    13. Wang, Limin & Song, Qiankun, 2020. "Pricing policies for dual-channel supply chain with green investment and sales effort under uncertain demand," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 79-93.
    14. Shu, Jinlong & Wu, Baowei & Xiong, Lianglin, 2022. "Stochastic stability criteria and event-triggered control of delayed Markovian jump quaternion-valued neural networks," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    15. Wang, Shuzhan & Zhang, Ziye & Lin, Chong & Chen, Jian, 2021. "Fixed-time synchronization for complex-valued BAM neural networks with time-varying delays via pinning control and adaptive pinning control," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    16. Sriraman, R. & Cao, Yang & Samidurai, R., 2020. "Global asymptotic stability of stochastic complex-valued neural networks with probabilistic time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 103-118.
    17. Zhao, Rui & Wang, Baoxian & Jian, Jigui, 2022. "Global μ-stabilization of quaternion-valued inertial BAM neural networks with time-varying delays via time-delayed impulsive control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 223-245.
    18. Li, Hong-Li & Zhang, Long & Hu, Cheng & Jiang, Haijun & Cao, Jinde, 2020. "Global Mittag-Leffler synchronization of fractional-order delayed quaternion-valued neural networks: Direct quaternion approach," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    19. Li, Hong-Li & Kao, Yonggui & Hu, Cheng & Jiang, Haijun & Jiang, Yao-Lin, 2021. "Robust exponential stability of fractional-order coupled quaternion-valued neural networks with parametric uncertainties and impulsive effects," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    20. Wang, Huamin & Wei, Guoliang & Wen, Shiping & Huang, Tingwen, 2021. "Impulsive disturbance on stability analysis of delayed quaternion-valued neural networks," Applied Mathematics and Computation, Elsevier, vol. 390(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:801-:d:358330. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.